In this theory, The Groundlessness of Infinity, I
introduce by three separate proofs a totally innovative concept regarding the
nature and relations among (pure) numbers. The applications of this wholly new
knowledge conclude to proving and solving major up-to-now unresolved problems,
e.g. the Riemann Hypothesis, Zeno's Paradoxes, the P Vs NP Problem, and other
major open issues. The core knowledge, as by the three above mentioned proofs
is that a number cannot be composite, it cannot bear any properties at all, and
there cannot be any kind of relationship among numbers. This leads to the
abolition of the numeric set of any kind, and subsequently to the abolition of
the numeric continuum and infinity. Nevertheless, it is the same logic that
abolishes infinity, which abolishes the notion of a supposed "ultimate
end", by introducing a new way of regarding the "limit" in
counting. The only logical basis I use about the proofs is the arithmetical
identity. Therefore in this theory, the new Foundations of Arithmetic are
established. Also, the Euclidean space has been proved here: the notion and the
entity of the straight line, the angle and the square have been proved. In
extension, the circle is proved to be a non-Euclidean object, and the proof of
the genuine calculation of the circle is given. This leads to answering the,
surprisingly, so far unanswered question of how a bicycle works.

In the Amazon
version of this book I have later on added one more crucial proof: “The
absolute proof of the gravitational field according to Albert Einstein”; as
well as two more equally valid books of mine.